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Power in High-dimensional testing Problems

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  • Anders Bredahl Kock
  • David Preinerstorfer

Abstract

Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, uniformly non-inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that can not be further improved with the power enhancement principle. When the dimensionality of the parameter space can increase with sample size, however, there typically is a range of "slowly" diverging rates for which every test with asymptotic size smaller than one can be improved with the power enhancement principle. While the latter statement in general does not extend to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.

Suggested Citation

  • Anders Bredahl Kock & David Preinerstorfer, 2017. "Power in High-dimensional testing Problems," Working Papers ECARES ECARES 2017-42, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/260442
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    Cited by:

    1. Anders Bredahl Kock & David Preinerstorfer, 2021. "Superconsistency of Tests in High Dimensions," Papers 2106.03700, arXiv.org, revised Jan 2022.
    2. Ge, S. & Li, S. & Linton, O., 2020. "A Dynamic Network of Arbitrage Characteristics," Cambridge Working Papers in Economics 2060, Faculty of Economics, University of Cambridge.
    3. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.
    4. David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    5. He, Yi & Jaidee, Sombut & Gao, Jiti, 2023. "Most powerful test against a sequence of high dimensional local alternatives," Journal of Econometrics, Elsevier, vol. 234(1), pages 151-177.
    6. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    high-dimensional testing problems; power enhancement principle; power enhancement component; asymptotic enhanceability; marginal LAN;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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